We know how to compute the entropy for states on such a code, following [1]} we find:
\(S_{\psi _{\rm eff}}(AA^\star )= - p_0 \ln p_0 - p_1 \ln p_1 + \left< \psi _{\rm eff} \right| \mathcal {L}_{AA^\star } \left| \psi _{\rm eff} \right>\) 
